Geodesic
$N=4$ superextension of the Liouville equation with quaternion structure
Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 2, pp. 230-243 
E. A. Ivanov; S. O. Krivonos. $N=4$ superextension of the Liouville equation with quaternion structure. Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 2, pp. 230-243. http://geodesic.mathdoc.fr/item/TMF_1985_63_2_a6/
@article{TMF_1985_63_2_a6,
     author = {E. A. Ivanov and S. O. Krivonos},
     title = {$N=4$ superextension of the {Liouville} equation with quaternion structure},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {230--243},
     year = {1985},
     volume = {63},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_63_2_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

An $N=4$ supersymmetric extension of the Liouville equation is constructed. It has internal $SU(2)\times SU(2)$ gauge symmetry and can be adequately formulated in terms of a real quaternion $N=4$ superfield on which definite conditions of Grassmann analytieity are imposed. Both the dynamical equations as well as the analyticity conditions follow from the zero-curvature representation on the superalgebra $su(1,1|2)$. It is shown that the obtained system is invariant with respect to transformations of the infinite-dimensional superalgebra of the $SU(2)$ superstring, the realization of these transformations differing from those previously known. The possible connection between the $N=4$ Liouville equation and the theory of the $SU(2)$ superstring is discussed.

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